New posts in baire-category

The inverse image of dense set is dense and of a comeager set is comeager?.

general-topology continuity descriptive-set-theory baire-category

Examples of closed subspaces of Baire spaces that fail to be Baire?

general-topology examples-counterexamples baire-category

Showing a set is nowhere dense in $C([0,1])$

real-analysis analysis banach-spaces baire-category holder-spaces

Is the union of two nowhere dense sets nowhere dense?

real-analysis general-topology baire-category

Is an NVS complete iff it is non meagre?

linear-algebra general-topology functional-analysis normed-spaces baire-category

What is the justification for these two steps in proof of Baire's theorem?

general-topology baire-category

Proving Baire's theorem: The intersection of a sequence of dense open subsets of a complete metric space is nonempty

real-analysis general-topology metric-spaces baire-category

Counterexample to the Converse of Baire's Category Theorem

real-analysis baire-category

Complement of meagre set contains a dense $G_\delta$ set

general-topology functional-analysis baire-category

$\lim_{n\to \infty}f(nx)=0$ implies $\lim_{x\to \infty}f(x)=0$ [duplicate]

real-analysis limits baire-category

Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?

general-topology metric-spaces baire-category

A classical problem about limit of continuous function at infinity and its connection with Baire Category Theorem

real-analysis baire-category

Simple question about Open Mapping Theorem's proof in Functional Analysis

general-topology functional-analysis linear-transformations baire-category

Is $[0,1]$ a countable disjoint union of closed sets?

real-analysis general-topology analysis baire-category

Let $X$ be an infinite dimensional Banach space. Prove that every Hamel basis of X is uncountable.

functional-analysis banach-spaces normed-spaces baire-category hamel-basis

Does the open mapping theorem imply the Baire category theorem?

functional-analysis set-theory banach-spaces axiom-of-choice baire-category

Your favourite application of the Baire Category Theorem

general-topology functional-analysis big-list baire-category